# Quantum Computing

If you were shrewd enough to invest $15,000 in Microsoft ten years ago you’d be a millionaire by now. The engine of growth that has driven the computer industry, and looks set to make Bill Gates the world’s first trillionaire, is no lucky fluke. Underpinning it have been sweeping advances in fundamental electronics. The first computers used bulky vacuum tubes and needed entire buildings to house them. Then in the 1960’s along came the transistor, which in turn gave way to the incredible shrinking microchip. But this is not the end of the story. Yet more exotic technologies are in the pipeline, and they promise to have as great an impact on the information industry as did the invention of the original computer.

The commercial success of computers stems from the fact that with each technological leap, the processing power of computers has soared and the costs have plummeted, allowing manufacturers to penetrate new markets and hugely expand production. The inexorable rise of the computer’s potency is expressed in a rough and ready rule known as Moore’s Law, after Gordon Moore, the co-founder of Intel. According to this dictum, the processing power of computers doubles every 18 months. But how long can it go on?

Moore’s law is a direct consequence of the “small is beautiful” philosophy. By cramming ever more circuitry into a smaller and smaller volume, faster information processing can be achieved. Like all good things, it can’t go on forever: there is a limit to how small electronic parts can be. On current estimates, in less than 15 years, chip components will approach atomic size. What happens then?

The problem is not so much with the particulate nature of atoms as such. Rather it lies with the weird nature of physics that applies in the atomic realm. Here, the dependable laws of Newtonian mechanics dissolve away into a maelstrom of fuzziness and uncertainty.

To understand what this means for computation, picture a computer chip as a glorified network of switches linked by wires in such a way as to represent strings of 1’s and 0’s – so-called binary numbers. Every time a switch is flipped, a bit of information gets processed; for example, a 0 becomes a 1. Computers are reliable because in every case a switch is either on or off; there can be no ambiguity. But for decades physicists have known that on an atomic scale, this either/or property of physical states is fundamentally compromised.

The source of the trouble lies with something known as Heisenberg’s uncertainty principle. Put crudely, it says there is an inescapable vagueness, or indeterminism, in the behaviour of matter on the micro-scale. For example, today an atom in a certain state may do such-and-such, tomorrow an identical atom could do something completely different. According to the uncertainty principle, it’s generally impossible to know in advance what will actually happen – only the betting odds of the various alternatives can be given. Essentially, nature is reduced to a game of chance.

Atomic uncertainly is a basic part of a branch of science known as quantum mechanics, and it’s one of the oddest products of twentieth century physics. So odd, in fact, that no less a scientist than Albert Einstein flatly refused to believe it. “God does not play dice with the universe,” he famously retorted. Einstein hated to think that nature is inherently and fundamentally indeterministic. But it is. Einstein notwithstanding, it is now an accepted fact that, at the deepest level of reality, the physical world is irreducibly random.

When it comes to atomic-scale information processing, the fact that the behaviour of matter is unreliable poses an obvious problem. The computer is the very epitome of a deterministic system: it takes some information as input, processes it, and delivers a definite output. Repeat the process and you get the same output. A computer that behaved whimsically, giving haphazard answers to identical computations, would be useless for most purposes. But try to compute at the atomic level and that’s just what is likely to happen. To many physicists, it looks like the game will soon be up for Moore’s Law.

Although the existence of a fundamental physical limit to the power of computation has been recognized for many years, it was only in 1981 that the American theoretical physicist Richard Feynman confronted the problem head-on. In a visionary lecture delivered at the Massachusetts Institute of Technology (MIT), Feynman speculated that perhaps the sin of quantum uncertainty could be turned into a virtue. Suppose, he mused, that instead of treating quantum processes as an unavoidable source of error to classical computation, one instead harnessed them to perform the computations themselves? In other words, why not use quantum mechanics to compute?

It took only a few years for Feynman’s idea of a “quantum computer” to crystallize into a practical project. In a trail-blazing paper published in 1985, Oxford theoretical physicist David Deutsch set out the basic framework for how such a device might work. Today, scientists around the world are racing to be the first to make it happen. At stake is far more than a perpetuation of Moore’s Law. The quantum computer has implications as revolutionary as any piece of technology in history. If such a machine could be built, it would transform not just the computer industry, but our experience of physical existence itself. In a sense, it would lead to a blending of real and virtual reality.

At the heart of quantum computation lies one of the strangest and most baffling concepts in the history of science. It is known technically as ‘superposition’. A simple example concerns the way an electron circles the nucleus of an atom. The rules of quantum mechanics permit the electron to orbit only in certain definite energy levels. An electron may jump abruptly from one energy level to a higher one if enough energy is provided. Conversely, left to itself, an electron will spontaneously drop down from a higher level to a lower one, giving off energy in the process. That is the way atoms emit light, for example.

Because of the uncertainty principle, it’s normally impossible to say exactly when the transition will occur. If the energy of the atom is measured, however, the electron is always found to be either in one level or the other, never in between. You can’t catch it changing places.

Now comes the weird bit. Suppose a certain amount of energy is directed at the atom, but not enough to make it jump quickly to an excited state. According to the bizarre rules of quantum mechanics, the atom enters a sort of limbo in which it is somehow in both excited and unexcited states at once. This is the all-important superposition of states. In effect, it is a type of hybrid reality, in which both possibilities – excited and unexcited atom – co-exist. Such a ghostly amalgam of two alternative worlds is not some sort of mathematical fiction, but genuinely real. Physicists routinely create quantum superpositions in the laboratory, and some electronic components are even designed to exploit them in order to produce desired electrical effects.

For 70 years physicists have argued over what to make of quantum superpositions. What really happens to an electron or an atom when it assumes a schizophrenic identity? How can an electron be in two places at once? Though there is still no consensus, the most popular view is that a superposition is best thought of as two parallel universes that are somehow both there, overlapping in a sort of dual existence. In the case of the atom, there are two alternative worlds, or realities, one with the electron in the excited state, the other with the electron in the unexcited state. When the atom is put into a superposition, both worlds exist side-by-side.

Some physicists think of the alternative worlds in a superposition as mere phantom realities, and suppose that when an observation is made it has the effect of transforming what is only a potential universe into an actual one. Because of the uncertainty principle, the observer can’t know in advance which of the two alternative worlds will be promoted to concrete existence by the act of observation, but in every case a single reality is revealed – never a hybrid world. Other physicists are convinced that both worlds are equally real. Since a general quantum state consists of a superposition of not just two, but an unlimited number of alternative worlds, the latter interpretation implies an outlandish picture of reality: there isn’t just one universe, but an infinity of different universes, existing in parallel, and linked through quantum processes. Bizarre though the many-universes theory may seem, it should not be dismissed lightly. After all, its proponents include such luminaries as Stephen Hawking and Murray Gell-Mann, and entire international conferences are devoted to its ramifications.

How does all this relate to computation? The fact that an atom can be in either an excited or an unexcited state can be used to encode information: 0 for unexcited, 1 for excited. A quantum leap between the two states will convert a 1 to a 0 or vice versa. So atomic transitions can therefore be used as switches or gates for computation.

The true power of a quantum computer comes, however, from the ability to exploit superpositions in the switching processes. The key step is to apply the superposition principle to states involving more than one electron. To get an idea of what is involved, imagine a row of coins, each of which can be in one of two states: either heads or tails facing up. Coins too could be used to represent a number, with 0 for heads and 1 for tails. Two coins can exist in four possible states: heads-heads, heads-tails, tails-heads and tails-tails, corresponding to the numbers 00, 01, 10 and 11. Similarly three coins can have 8 configurations, 4 can have 16 and so on. Notice how the number of combinations escalates as more coins are considered.

Now imagine that instead of the coins we have many electrons, each of which can exist in one of two states. This is close to the truth, as many subatomic particles when placed in a magnetic field can indeed adopt only two configurations: parallel or antiparallel to the field. Quantum mechanics allows that the state of the system as a whole can be a superposition of all possible such “heads/tails” alternatives. With even a handful of electrons, the number of alternatives making up the superposition is enormous, and each one can be used to process information at the same time as all the others. To use the jargon, a quantum superposition allows for massive parallel computation. In effect, the system can compute simultaneously in all the parallel universes, and then combine the results at the end of the calculation. The upshot is an exponential increase in computational power. A quantum computer with only 300 electrons, for example, would have more components in its superposition than all the atoms in the observable universe!

Achieving superpositions of many-particle states is not easy (the particles don’t have to be electrons). Quantum superpositions are notoriously fragile, and tend to be destroyed by the influence of the environment, a process known as decoherence. Maintaining a superposition is like trying to balance a pencil on its point. So far physicists have been able to attain quantum computational states involving only two or three particles at a time, but researchers in several countries are hastily devising subtle ways to improve on this and to combat the degenerative effects of decoherence. Gerard Milburn of the University of Queensland and Robert Clark of the University of New South Wales are experimenting with phosphorus atoms embedded in silicon, using the orientation of the phosphorus nuclei as the quantum equivalent of heads and tails.

The race to build a functioning quantum computer is motivated by more than a curiosity to see if it can work. If we had such a machine at our disposal, it could perform tasks that no conventional computer could ever accomplish. A famous example concerns the very practical subject of cryptography. Many government departments, military institutions and businesses keep their messages secret using a method of encryption based on multiplying prime numbers. (A prime number is one that cannot be divided by any other whole number except one.) Multiplying two primes is relatively easy. Most people could quickly work out that, say, 137 x 291 = 39867. But going backwards is much harder. Given 39867 and asked to find the prime factors, it could take a lot of trial and error before you hit on 137 and 291. Even a computer finds the reverse process hard, and if the two prime numbers have 100 digits, the task is effectively impossible even for a supercomputer.

In 1995 Peter Shor, now at AT&T Labs in Florham Park, New Jersey, demonstrated that a quantum computer could make short work of the arduous task of factorising large prime numbers. At this stage governments and military organizations began to take an interest, since it implied that a quantum computer would render many encrypted data insecure. Research projects were started at defense labs such as Los Alamos in New Mexico. NATO and the U.S. National Security Agency began pumping millions of dollars into research. Oxford University set up a special Centre for Quantum Computation.

Soon mathematicians began to identify other problems that looked vulnerable to solution by quantum computation. Most of them fall in the category of search algorithms – various forms of finding needles in haystacks. Locating a friend’s phone number in a directory is easy, but if what you have is a number and you want to work backwards to find the name, you are in for a long job.

A celebrated challenge of this sort is known as the travelling salesman problem. Suppose a salesman has to visit four cities once and only once, and the company wishes to keep down the travel costs. The problem is to determine the routing that involves minimal mileage. In the case of four cities, A, B, C and D, it wouldn’t take long to determine the distance traveled in the various alternative itineraries – ABCD, ACBD, ADCB and so on. But for twenty cities the task becomes formidable, and soars further as additional cities are added.

It is too soon to generalise on how effectively quantum computers will be able to short-circuit these sorts of mega-search problems, but the expectation is that they will lead to a breathtaking increase in speed. At least some problems that would take a conventional supercomputer longer than the age of the universe should be solvable on a quantum computer in next to no time. The practical consequences of this awesome computational power have scarcely been glimpsed.

Some scientists see an altogether deeper significance in the quest for the quantum computer. Ultimately, the laws of the universe are quantum mechanical. The fact that we normally encounter weird quantum effects only at the atomic level has blinded us to the fact that – to paraphrase Einstein – God really does play dice with the universe. The main use of computers is to simulate the real world, whether it is a game of Nintendo, a flight simulator or a calculation of the orbit of a spacecraft. But conventional computers recreate the non-quantum world of daily experience. They are ill suited to dealing with the world of atoms and molecules. Recently, however, a group at MIT succeeded in simulating the behaviour of a quantum oscillator using a prototype quantum computer consisting of just four particles.

But there is more at stake here than practical applications, as first pointed out by David Deutsch. A quantum computer, by its very logical nature, is in principle capable of simulating the entire quantum universe in which it is embedded. It is therefore the ultimate virtual reality machine. In other words, a small part of reality can in some sense capture and embody the whole. The fact that the physi al universe is constructed in this way – that wholes and parts are mutually enfolded in mathematical self-consistency – is a stunning discovery that impacts on philosophy and even theology. By achieving quantum computation, mankind will lift a tiny corner of the veil of mystery that shrouds the ultimate nature of reality. We shall finally have captured the vision elucidated so eloquently by William Blake two centuries ago:

And a Heaven in a wild flower,

Hold infinity in the palm of your hand,

And eternity in an hour.